handbook of modern sensors

130 4 Optical Components of Sensors
system. In any event, the so-called photometric characteristics of the optical system
should be taken into account. Such characteristics include light, emittance, luminance,
brightness, and so forth.
To measure radiant intensity and brightness, special units have been devised.
Radiant flux (energy emitted per unit time), which is situated in a visible portion of the
spectrum, is referred to as luminous flux. This distinction is due to the inability of the
human eye to respond equally to like power levels of different visible wavelengths.
For instance, one red and one blue light of the same intensity will produce very
different sensations; the red will be perceived as much brighter. Hence, comparing
lights of different colors, the watt becomes a poor measure of brightness and a special
unit called a lumen was introduced. It is based on a standard radiation source with
molten platinum formed in a shape of a blackbody and visible through a specified
aperture within a solid angle of one steradian. A solid angle is defined in a spherical
geometry as
ω = A r 2 , (4.13)
where r is the spherical radius and A is the spherical surface of interest. When A = r,
the unit is called a spherical radian or steradian (sr) (see Table 1.7).
Illuminance is given as
E = dF
dA ; (4.14)
that is, a differential amount of luminous flux (F ) over a differential area. It is most
often expressed in lumens per square meter (square foot), or foot-meter (foot-candle).
The luminous intensity specifies flux over solid angle:
I L = dF
dω ; (4.15)
most often, it is expressed in lumens per steradian or candela. If the luminous intensity
is constant with respect to the angle of emission, Eq. (4.15) becomes
I L = F ω . (4.16)
If the wavelength of the radiation varies but the illumination is held constant, the
radiative power in watts is found to vary. A relationship between illumination and
radiative power must be specified at a particular frequency. The point of specification
has been taken to be at a wavelength of 0.555 µm, which is the peak of the spectral
response of the human eye. At this wavelength, 1 W of radiative power is equivalent
to 680 lumens. For the convenience of the reader, some useful terminology is given
in Table 4.1.
In the selection of electro-optical sensors, design considerations of light sources
are of prime concern. A light source will effectively appear as either a point source
or as an area source, depending on the relationship between the size of the source
and the distance between the source and the detector. Point sources are arbitrarily
defined as those whose diameter is less than 10% of the distance between the source